﻿ 适于时变幅值分析的直升机黏弹减摆器模型<sup>*</sup>
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A model of helicopter elastomeric damper for time varying amplitude analysis
WU Jing, HU Guocai, LIU Xiangyi
Aeronautical Foundation College, Naval Aviation University, Yantai 264001, China
Received: 2017-10-16; Accepted: 2017-11-23; Published online: 2018-01-16 13:09
Corresponding author. HU Guocai, E-mail: guocaihu11@sina.com
Abstract: The existing elastomeric damper models commonly introduce dynamic amplitude parameter for applying to wide amplitude situation. It is inconvenient to time domain analysis of helicopter rotor-fuselage coupled dynamic stability on account of the dynamic amplitude changing in time domain. Aimed at this problem, the calculation methods of dynamic amplitude parameter were given for single and double frequency excitation cases while the lagging damping ratio is little. The amplitude curves calculated by the method describe the response amplitudes well while the system is in the state of convergence, neutral stable, or divergence. The improved model of elastomeric damper was used for nonlinear time domain analysis of helicopter ground resonance. The calculation method of excitation moment at blade was given for exciting the regressive lagging mode responses accurately. For different rotor speeds and complex modulus states, the response amplitudes excited by the excitation moment determined by the moment calculation method were compared with the desired values, and the maximum error is under 6%. After the regressive lagging mode responses are analyzed, it is known that the regressive lagging mode responses decay faster than the linearization results, and its modal damping increases in time domain due to the elastomeric damper nonlinearity while system is stable.
Keywords: helicopter     elastomeric damper     nonlinear     time domain analysis     ground (air) resonance

1 黏弹减摆器改进模型

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1.1 单频激振条件

 图 1 不同稳定情况下的单频时域响应 Fig. 1 Single frequency response in time domain at different stable situations

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1.2 双频激振条件

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1Ω强迫振动在摆振阻尼较小的情况下，强迫振动幅值可表示为

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 图 2 不同稳定情况下的双频时域响应 Fig. 2 Double frequency response in time domain at different stable situations

 图 3 黏弹减摆器时域响应计算流程 Fig. 3 Calculation flow of elastomeric damper time domain response

2 计入黏弹减摆器的地面共振分析 2.1 计入黏弹减摆器的地面共振模型

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2.2 仿真分析主要参数

 图 4 复模量对比结果 Fig. 4 Comparison of complex modulus

 参数 数值 桨叶片数 4 桨叶质量/kg 42.3 桨叶对摆振铰静矩/(kg·m) 123.7 桨叶对摆振铰惯性矩/(kg·m2) 457 摆振铰外伸量/m 0.23 减摆器到摆振铰距离/m 0.35 机体纵向当量质量/kg 2 000 机体纵向固有频率/Hz 1 机体纵向当量阻尼/(N·s·m-1) 1 000 机体横向当量质量/kg 800 机体横向固有频率/Hz 1.5 机体横向当量阻尼/(N·s·m-1) 500

2.3 地面共振仿真分析

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 图 5 减摆器响应幅值变化情况 Fig. 5 Response amplitude of damper

 图 6 线性系统的摆振后退型模态特性 Fig. 6 Regressive lagging modal features of linear system

 图 7 第1个黏弹减摆器的位移响应 Fig. 7 Displacement response of the first elastomeric damper
 图 8 第1个黏弹减摆器的功量图 Fig. 8 Force-displacement curves of the first elastomeric damper

 图 9 旋翼摆振后退型时域响应 Fig. 9 Time domain response of rotor regressive lagging mode
 图 10 旋翼摆振后退型阻尼随时间变化情况 Fig. 10 Variation of rotor regressive lagging modal damping with time

3 结论

1) 针对小摆振阻尼比的情况，给出了单频及双频条件下黏弹减摆器模型中动幅值参量的计算方法，采用该方法计算系统在收敛、中性稳定及发散3种情况下的幅值曲线能较好地反映响应幅值在时域上的变化趋势，说明该方法可使带动幅值参量的黏弹减摆器模型用于直升机旋翼/机体耦合动稳定性时域分析。

2) 给出了计入非线性黏弹减摆器后，激出旋翼摆振后退型模态所需激振力矩的计算方法，在不同转速不同复模量状态下，采用该方法确定的激振力矩对桨叶进行激振激出的响应幅值与预期值误差不超过6%，说明了所述方法的准确性。

3) 将改进后的黏弹减摆器模型用于直升机地面共振时域分析，对摆振后退型响应进行分析可知，系统稳定时，与线性化结果相比，计入黏弹减摆器非线性后，旋翼摆振后退型响应衰减更快，其模态阻尼在时域上呈增加趋势。

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#### 文章信息

WU Jing, HU Guocai, LIU Xiangyi

A model of helicopter elastomeric damper for time varying amplitude analysis

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(8): 1665-1671
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0633